Dynamic pattern theory - some implications for therapeutics.

Dynamic Pattern Theory--Some Implications for Therapeutics The key constructs of the Dynamic Pattern Theory (DPT) of movement coordination are summarized in this article. Coordination is defined as the process by which movement components are sequenced and organized temporally, and their relative magnitudes determined, in order to produce a functional movement pattern, or synergy. Dynamic Pattern Theory addresses questions related to how functional movement patterns are learned and reliably produced. The theory's basic tenets, its predictions about how motor acts are organized, and the implications of these tenets for motor learning and the recovery of motor function are described briefly. Emphasis is given to defining the constructs of the approach and to discussing their potential use for assessing the coordination of functional motor acts.

A major problem faced by the nervous system in the coordination of functional motor acts has been referred to as the "degrees-of-freedom" problem: that is, how are the relatively limited sets of observed movement patterns reliably produced given the nearly infinite combinations of possible states or values that the neural, muscular, and skeletal components of the motor system can assume? [1] Consider, for example, the hand reaching to a specific location in space. This act minimally requires coordination of scapular, glenohumeral, elbow, radioulnar, wrist, and finger joints. Any arbitrary sequencing or relative timing of joint motions will be unlikely to result in successful performance. In addition, much redundancy exists in the muscular control of any one of these joints (eg, the elbow can be flexed directly by either isolated or combined action of the biceps, brachialis, or brachioradialis muscles or indirectly by the action of muscles of the glenohumeral joint through reactive forces that act across the elbow). [2] Furthermore, the neural control of any one of these muscles is far from simple, involving different motor unit types, different reflex pathways, etc. Yet, the potentially myriad combinations and temporal orderings of movement components give way to a very few and distinct number of movement patterns. A major goal of movement scientists, then, is to discover how this effective compression from many to only few degrees of freedom is achieved. [1]

A similar problem exists for scientists seeking to understand how the degrees-of-freedom problem is solved by the nervous system. Given the choice of a particular behavior to study (eg, human reaching, crayfish locomotion), we must choose a model system and a particular scale of observation on which to concentrate our efforts (ie, a few neurons, entire neural networks, individual muscles or joints, or the entire organism). It is necessary to decide which variables to manipulate experimentally and which to measure as indices of a system's performance or response. Because it is usually impossible to study all possible variables, and because of potential limitations of modeling complex behaviors from an analysis of a select number of components, these decisions are not trivial. This fact can be attested to by those involved in the search for the central pattern generators underlying innate motor patterns such as locomotion. [3] Even if all conceivable variables could be measured, organizing the resulting mass of potential information to form a coherent picture would be overwhelming. Therefore, one's choice must be both selective and guided by a strategy.

An equally difficult task is faced by those who teach complex motor skills or even the most basic movement patterns to patients with movement dysfunction. As therapists, we are faced with the difficult task of choosing from among a wealth of movement-related variables in order to find the best index of performance along the dimension of interest. Our current inability to document the effectiveness of many treatment procedures may be due, in part, to inadequate or inappropriate measures of performance rather than the failure of a particular treatment approach. In addition, when teaching motor skills to patients, we must identify those variables that can be manipulated to facilitate optimal motor performance. What information is available to guide such decisions?

For researchers, theories or models of the system of interest provide guidelines for determining which variables to consider and which questions to ask about a particular phenomenon. Theories of motor control and motor development also have been used by therapists to guide the development of specific treatment paradigms [4-6] and, to a lesser extent, the selection of measures for evaluating motor performance. Yet, in many such instances, "theory" consists of many loosely connected facts and assumptions rather than a coherent framework for generating and testing hypotheses and organizing knowledge. This is especially true of many therapists who treat patients with movement dysfunction, where the theoretical rationale for the methods used is often implicit at best. Yet, our theoretical perspective will greatly influence what we measure, which variables we choose to manipulate, and the conclusions we form. Thus, it is important for scientists and clinicians alike to recognize the assumptions underlying their work and how their work is influenced by such assumptions. In this article, a relatively new theoretical approach is presented that provides (1) new insights about how the nervous system may solve the previously mentioned degrees-of-freedom problem and (2) guidelines for identifying critical variables for assessing motor coordination and influencing pattern change.

Dynamic Pattern Theory

Much of the scientific work on animal movement has involved modeling particular aspects of motor behavior with specific mechanisms and a search for the material embodiment of such mechanisms in related experimental work. For example, coordination of the many components involved in performing an act such as locomotion or chewing is often assumed to have its basis in detailed neural circuits located in the spinal cord or brain stem. [7,8] The organization of such networks is thought to directly embody the pattern of coordination to be produced. Thus, simply "turning on" the circuit is considered sufficient to produce the basic features of the movement pattern. [7] More complex or learned motor acts are believed by many to be programmed through more diffusely organized neural networks that are distributed throughout many different brain regions. [9-12] In such cases, the analogy of the computer program is frequently used as an appropriate model for how the nervous system organizes the components and features of such movements.

The search for neural mechanisms underlying motor behavior is certainly important. However, whether that pursuit alone is sufficient to understand how motor patterns are generated and how they change is questionable. [13] For example, the neural mechanisms responsible for generating locomotor patterns in animals can vary substantially from one animal species to another, as does the material structure of the limbs themselves (eg, compare the cat and the cockroach). Yet, the locomotor synergies appear to be very similar across species, despite the diversity of structure (eg, the relative durations of the stance and swing phases, the effect of specific sensory inputs on the timing of the various phases of the gain cycle). [14] What factors account for the common properties of locomotor coordination? Is it possible that principles or laws of coordination exist that transcend the particular material structures being coordinated?

Dynamic Pattern Theory was developed by Kelso and colleagues [15-18] based on Haken's Synergetics [19] as an attempt to determine whether general principles of pattern generation could be identified that are common to a variety of animal motor behaviors and independent of the structures producing those behaviors. Although it is recognized that the structure of neural networks provides the supporting framework for pattern generation, the research spawned by DPT suggests that principles of pattern organization exist that transcend the specific material structure of such networks. The theory emphasizes identification of observable macroscopic variables and the study of their dynamics in order to characterize movement patterns and their stability quantitatively. Once such parameters are identified, a number of measures of pattern stability are well defined and can be used to characterize the process of pattern change.

It should be emphasized that our use of the term "macroscopic" is relative to the scale of observation of the model system being studied. For example, a muscle's activation states are macroscopic with respect to the properties of motor units comprising the muscle, whereas these states are microscopic relative to a variable that describes the coordination of two such muscles. Unlike some contemporary theories of motor control, which address issues of coordination primarily or entirely at a neural level, [7] the emphasis of DPT on discovering general principles or laws of coordination makes the theory potentially applicable at any scale of observation. [20] Thus, the theory may provide insights that are as important and useful to the clinician working on the scale of the whole organism as they are to the researcher studying neural pattern generators for locomotion.

In what follows, the basic constructs of the theory are presented individually. A discussion of possible implications for patient rehabilitation follows each presentation. In an attempt to provide a coherent thread throughout the discussion, the "bunny-hop" pattern of locomotion that is frequently observed in children with spastic diplegia will be used to illustrate the application of the theory's constructs to therapeutics.

Order Parameters 

As noted previously, DPT was derived from Synergetics, a physical theory of self-organization and pattern formation. [19] Synergetics involves the study of physical, chemical, and biological systems that are composed of a large number of components or degrees of freedom, such as lasers and slime molds. Although such systems are significantly less complex than most biological systems, they are composed of very many components. Therefore, principles derived from the study of such systems can provide important insights about how many interacting components cooperate to produce complex structural or behavioral patterns.

One strategy for understanding the coordination of a system's components is to study their behavior individually and their interactions with other components in the face of systematic experimental manipulations. Even for these comparatively simple systems, however, an understanding of their coordinated behavior from such an analysis alone has proved extremely difficult to achieve. [19] This difficulty is due, in part, to the large number of components and relationships that would have to be evaluated. An alternative and often more fruitful initial approach has been to identify a smaller set of variables that are defined macroscopically with respect to the system's many components and that can be used to characterize the system's observed behavioral patterns. In theory, the values that these variables take on at any point in time are assumed to correspond to the system's behavioral patterns. Discovering such variables for movement coordination would provide us with a small and manageable set of quantitative measures that could be used to study a system's behavioral dynamics, or how the system changes its patterns and the stability of those patterns. In DPT, such macroscopic variables are referred to, after Synergetics, as the system's order parameters. The identification of a system's order parameters allows us to (1) discover the conditions that precipitate pattern change, (2) determine the effect of different parameter manipulations on a pattern's stability, and (3) provide a basis for precise and formal modeling of a behavior's coordinative patterns and the generation of predictions about system behavior that can be tested experimentally.

Recent experiments on human bimanual coordination [15,21,22] provide a concrete example of this premise. As a basis for understanding how patterns of coordination are generated and the process by which such patterns change, a relatively simple system, two hands rhythmically oscillating about the wrists, was studied. [15] In this paradigm, subjects are asked to rhythmically flex and extend each hand at a particular movement frequency, while simultaneously maintaining a specified time lag between movement of the hands. [15,22] Although the task is relatively simple, coordination of the hands involves the cooperative interaction of many components, ie, the wrist extensor and flexor muscles across both limbs, and the numerous neural components that affect their timing and level of activation.

One could attempt to characterize this coordination by studying any number of variables, including movement displacement, period, velocity, or acceleration, or one or more electromyographic (EMG) measures of the muscles involved. Although all are movement-related variables, none of them reflect directly how the hands are coupled in performing the task. However, one variable that does reflect this coordination is the relative phase ([Phi]), or timing of one hand's motion with respect to the other. A cycle-to-cycle estimate of relative phase can be obtained by determining where the right hand, for example, reaches its maximum displacement in extension with reference to the corresponding cycle (ie, the time from one extension maximum to the next) of the left hand's motion. If maximum extension occurs simultaneously in the two hands, the relative phase of their motions is zero, and the hands are said to be coordinated in-phase. When maximum extension of the left hand occurs simultaneously with maximum flexion of the right hand in a 1:1 frequency relation, relative phase is 0.5, and the hands are coordinated perfectly anti-phase.

A more continuous estimate of this variable, based on each sample of movement, can be derived from each hand's phase diagram. The phase diagram is a plot of each hand's position versus its velocity at every instance in time and is illustrated for a few data points from one cycle of movement in Figure 1. To facilitate calculation, both the velocity and displacement are normalized on the interval [-1, 1]. If the hand's motion is approximately sinusoidal, a phase angle can be calculated for each data sample. For the first sample in Figure 1A, for example, the left hand's phase of motion can be estimated as the angle ([Phi.sub.L]) formed between the positive x-axis and a straight line drawn between the origin and the sample coordinate of interest. This can then be repeated for each successive sample value. In general, the phase angle will take on values between 0 and 360 degrees throughout the cycle of movement. The phase angle, then, describes where in the hand's cycle of motion it is currently located. Likewise, the phase angle [([Phi].sub.R]) can be calculated for corresponding sample values of the right hand's motion (Fig. 1B). The difference between the phase angles for the two hands at each sample value (ie, point in time) gives the relative phase of their motions, (ie,[[Phi]=[Phi].sub.R.-[Phi].sub.L]) in degrees (see article by Scholz and Kelso [21] for a more exact definition of the phase calculation). For example, at sample 1 of our example, the left hand's phase angle is approximately 210 degrees, whereas that of the right hand is approximately 30 degrees. The relative phase of their motions, then, is

[Phi is nearly equal to 210[degrees] - 30[degrees] is nearly equal to 180[degrees]]

The hand's motions are anti-phase with one another, flexion of one hand occuring while the other hand extends. Therefore, the coordination between the two hands, and potentially any two components, can be characterized quantitatively be determining their relative phase of motion. With this measure in hand, the stability or variability of coordination patterns can be determined.

Examples from the bimanual coordination experiments of both cycle and individual sample estimates of relative phase are provided in Figure 2 (notice that the second measure [Fig. 2C] reveals greater detail about a pattern's dynamics). This figure illustrates a transition or switching from the antiphase ([Phi]=0.5 or 180[degrees]) to the in-phase ([Phi]=0.0 or 0[degrees]) pattern of hand coordination, which will be discussed below.

Therapeutic implications. For therapist attempting to induce a change in the pattern of coordination exhibited by a patient, identification of relevant order parameters for the motor task provides a means of quantifying movement patterns and studying how they change under different conditions. Consider, as an example, the child with cerebral palsy who locomotes using a "bunny-hop" or hopping pattern (ie, a quadrupedal pattern of interlimb coordination in which both extremities of the pelvic or shoulder girdles move nearly in phase with one another, while one girdle moves out of phase with the other). One goal of therapy might be to facilitate a more reciprocal pattern of lower extremity coordination, to approximate a more normal creeping pattern. In this case, the relative phase of hip movement could be a useful order parameter for this task. If so, measurement of this variable would allow changes in the pattern to be documented quantitatively as treatment or development proceeds, as well as a determination of how different conditions affect the pattern's dynamics. This measurement could be accomplished with videography, using two synchronized cameras, or by applying knee pads that contain contact switches. The relative proportion, for example, of the right limb's creeping cycle, from one limb touchdown to the next, at which the left limb contacts the ground could be measured for multiple movement cycles and used to estimate the degree to which the relative phase of motion of the two lower extremities approaches 0.5, or an anti-phase pattern. The relative phasing of diagonal limbs might also be instructive about changes in the pattern with treatment (see "Pattern Stability and Order Parameter Fluctuations").

Identifying potential order parameters for other behavior might be more difficult, as in the coordination of muscles or joints of the upper extremity during reaching. Her again, the relative timing or phase of joint motions may be an appropriate order parameter. Because more than two joints are coordinated in this task, however, more than one order parameter may be required to fully characterize reaching patterns. On the other hand, experimental study might reveal that coupling of the motions of some joint pairs does not change, or does so unsystematically with changing task conditions, and thus does not reflect qualitative changes in the overall reaching pattern. As such, these particular relative phase measures would not be useful for characterizing the coordination of reaching per se. Work currently underway on patterns of coordination for the act of manual lifting suggests that only a few of the many relative timing relationships between the participating joints appear to be necessary to characterize lifting patterns (JP Scholz, work in progress). This finding may also apply to other complex acts such as reaching. [23,24] Alternatively, it is possible that variables other than relative phase may be more appropriate order parameters for a task such as reaching (eg, some variable related to the hand's overall trajectory or its smoothness). [25-27] This would need to be determined experimentally. Nevertheless, identification of the order parameters for a particular task would greatly enhance our ability to evaluate the effect of therapeutic interventions on movement coordination and the natural course of recovery.

Control Parameters and

Spontaneous Pattern Transitions

The identification of order parameter(s) for a particular behavior typically is not a simple matter. One strategy that is often helpful is to get the system to undergo a spontaneous pattern change, or pattern transition. Pattern transitions often occur in nature spontaneously when certain nonspecific factors are manipulated appropriately. "Nonspecific" indicates that the variable being changed does not specify to the system what pattern it should adopt. A change is such a variable is seen to provide a sufficient condition for pattern change to occur (see "Self-Organization, Behavioral Information, and Learning"). For example, if a horse is forced to increase its velocity of locomotion sufficiently during trotting, a transition to galloping is likely to take place. The increase in velocity, and the increased neuromuscular activation required to bring it about, does not specify the new pattern of interlimb coordination. Nonspecific factors that, when changed continuously, take a system through its repertoire of states (ie, state of being or condition) or patterns are referred to in DPT as control parameters. When a control parameter reaches a critical value (eg, a critical velocity of locomotion), the system exhibits a transition to a new or different pattern of coordination, providing the conditions necessary for identifying a system's order parameters.

Potential order parameters may be selected initially on the basis of theoretical or biomechanical arguments or the results of studies of similar systems. Observing the behavior of candidate variables in the region of a pattern transition may allow one to determine which of these variables is an order parameter for the behavior. By definition, a correspondence exists between an order parameter's values and a system's behavioral patterns. Thus, when a particular coordination pattern (eg, flexion of one forelimb during extension of the other in troting) is stable, the value of the system's order parameters should also remain relatively stable. Likewise, a qualitative change in the movement pattern (eg, to simulataneous flexion of both forelimbs in galloping) is expected to be accompanied by a similar change in the value of a system's order parameter(s). If the behavior of one or more candidate variables meets this criterion, then they may be considered order parameters for that system. Variables that remain relatively constant during a pattern transition, or that change continuously (eg, hip displacement) despite the stable performance of a particular pattern, could be rejected. [28]

Once again, this strategy for identifying a system's order parameters will work only if we elicit a pattern transition. Doing so requires that we find the appropriate control parameter(s). For example, consider the bimanual coordination experiments of Kelso and colleagues. [15,16,21] Whe subjects moved their hands at low movement frequencies (paced by an audible metronome), either an anti-phase (flexion of one hand occurring simultaneously with extension of the other) or in-phase (flexion or extension of both hands occurring simultaneously) pattern of coordination between the hands could be produced. However, increasing the frequency of movement gradually led to a loss of stability of the anti-phase pattern so that, at a critical frequency, a transition occurred to the in-phase pattern (Fig. 2A). The transition occurred spontaneously because subjects were asked not to intentionally switch between patterns, but to try and maintain the ongoing pattern of bimanual coordination while increasing their movement frequency. The frequency of hand movement was an effective control parameter. Once this spontaneous pattern transition could be reliably produced experimentally, several movement-related variables could then be evaluated as possible order parameters for this model system. One such variable, the relative phase of motion between the two hands, also remained relatively constant in value during the performance of a particular bimanual pattern (Figs. 2B and 2C before and after the transition) (ie, [Phi] [is nearly equal] 180[degrees] during anti-phase coordination and [Phi] [is nearly equal] 0[degree] during in-phase coordination), and there was a cooresponding change in the value of the relative phase (180[degrees] [right arrow] 0[degree] at the pattern transition. Therefore, this variable can be considered an appropriate order parameter for this model system.

It is important to point out that if these experiments had not included relatively high movement frequencies, observation of this pattern transition would have been unlikely. Similarly, a transition from the interlimb coordination pattern for walking to one for trotting or galloping would not be likely if a horse were observed only during locomotion at very low speeds. Thus, in order to identify whether a particular variable is a control parameter for a behavior, and to use that variable to promote a pattern change, the variable must be taken through a sufficient range of its values. Other examples of spontaneous pattern transitions occurring when a system control parameter reaches a critical value may be found in work on human locomotion, [29] hand-elbow, [30] and hand-foot coordination patterns. [31] In the latter two examples, a key control parameter appears to be the spatial position of the forearm. That is, the stability of a particular pattern of coordination (eg, wrist flexion-ankle dorsiflexion or wrist flexion-ankle plantar flexion) was found to be dependent on whether the forearm was pronated or supinated. [30,31]

Note also that the word "control" has a different meaning in this context than its typical connotation in motor control theory, where coordination often is assumed to result from the implementation of specific control strategies (eg, instructions in a motor program). [7] Once again, a change in the value(s) of a system's control parameter(s) is not viewed in DPT as specifying directly to a system which pattern it should adopt. Instead, such changes are thought to provide the necessary conditions for the system to change patterns spontaneously, depending on each pattern's relative stability. Thus, control may be thought of as the process of scaling the neuromuscular components up or down on some variable such as position, stiffness, force, or speed.

Not all system variables are likely to be equally effective at producing a spontaneous change in the pattern of coordination. Thus, for example, artificially increasing the mass of the hands by applying increasingly large loads does not appear to lead directly to a change in the pattern of bimanual coordination. This manipulation does appear, however, to interact with movement frequency, so that the transition occurs at a lower frequency than normal when the load is high. [15] Which variables may act as control parameters for a behavior, and which of these variables are most effective in producing pattern change, remains to be determined.

Studies of spontaneous pattern change also allow us to first identify the intrinsic dynamics of a system's coordination patterns vis-a-vis the dynamics of its order parameter(s) so that the influence of intentions may be better understood. "Intrinsic" refers to the fact that the patterns of interest are basic ones that do not require learning (although they may have been learned previously) and can be produced without specific intent or conscious effort on the part of the subject (although they may be produced intentionally as well). In DPT, the dynamics of intentional pattern change are hypothesized to result from a modification of a system's intrinsic coordination dynamics. (Recall that by "dynamics" we refer to the nature of change from one pattern to another or a change in the stability of a given pattern). Thus, for example, in order to fully understand the dynamics of an intentional switch between the anti-phase and in-phase patterns of coordination or vice versa, the intrinsic dynamics (ie, those related to spontaneous pattern transitions) for this model system must first be understood. This point has been recently supported both experimentally and through model simulations of intentional bimanual transitions. [32,33] Theoretically, the same argument applies to an understanding of the pattern dynamics for any system.

Therapeutic implications. Suppose that we wish to identify the order parameters for a particular behavior so that we can better quantify changes in the patterns of coordination exhibited by our patients. As we have seen, one strategy for doing so is to elicit a pattern transition and observe the behavior of candidate variables in the transition region. In therapy, eliciting a change in the pattern of coordination is frequently our goal, yet is often difficult to achieve, particularly with neurologically impaired patients. In such instances, therefore, it may be necessary to use the results of basic research on similar coordination patterns as a guide to determine what the order parameters are likely to be. For example, relative phase or timing variables are likely to be important order parameters for many motor behaviors, although other variables may also be important for some behaviors. This hypothesis is supported not only by the bimanual experiments reported previously, but also by simulations of theoretical models of this system [18] and by recent experimental work on similar behaviors. [30,34,35] Once again, videography may be a useful data collection tool from which such parameters could be measured quantitatively.

However, DPT also provides guidelines for how to promote pattern change. Two points are worth emphasis here. First, in order to elicit movement pattern transitions automatically, it is necessary to identify and manipulate the appropriate control parameters. Unsuccessful treatment may be more often the result of a failure to explore a sufficient number of parameters in order to determine a system's control parameters than of a lack of potential for patient recovery. Second, identified control parameters must be taken through a sufficient range of values so that the critical value for a pattern transition is reached. Similarly, the effect of interactions among variables should be fully explored in order to enhance the likelihood of producing the desired pattern transition or, in the case of an abnormal pattern, preventing it from occurring.

For the child with cerebral palsy who bunny-hops, a goal of therapy may be to facilitate reciprocal creeping. One possible approach would be for the therapist to directly control each of the child's lower extremities as he or she actively locomotes, restraining forward motion of one limb while moving the other forward, then reversing this procedure to produce a reciprocal pattern, a type of patterning. One way to look at this procedure is that the therapist is directly manipulating the relative timing of lower extremity motions, an order parameter for the behavior, in the hope that the resulting change in sensory input will lead to an actual pattern change centrally. Alternatively, a therapist may search for control parameters that can be manipulated to facilitate the emergence of the desired pattern. For instance, the therapist may take advantage of insights derived from basic research on quadrupedal animal locomotion, [14] manipulating the amount of loading or the degree of hip extension of the lower extremities. Controlling the patient's pelvis from behind and above, the amount of force exerted through the weight-bearing hip and its degree of extension could be controlled and might lead to a more normal reciprocal pattern. The control parameter here actually may be the degree of weight shift produced during the task. Without adequate weight shift, the in-phase pattern may be the only stable pattern available to the system. Thus, the focus of training would be on the attainment of greater weight shift during this and related activities, rather than on the locomotor pattern per se.

Children who exhibit the hopping pattern tend to have lower extremities that are extremely stiff. That is, the amount of resistance opposing passive joint or limb displacement or active agonist contraction is greater for a given amount of displacement than would normally be found. Drawing a parallel to our studies on bimanual coordination, limb stiffness may be an important control parameter such that, when stiffness is high, only the in-phase pattern of coordination is stable. The organization of spinal networks required to produce the anti-phase pattern of coordination involves the simultaneous activation of nonhomologous muscles in the two limbs, which may be more difficult than activating homologous muscles simultaneously. The organization of interlimb influences required to support the anti-phase pattern may not be stable when limb stiffness is high, a possibility that we are currently investigating. In any case, if this idea has some validity, then procedures that decrease limb stiffness might result in the ability to produce a more normal creeping pattern. There is some indirect support for this idea (eg, less-involved children can often reciprocate when creeping at relatively slow movement speeds, usually associated with less limb stiffness, but switch to a hopping pattern when they become excited or increase their speed of locomotion). Moreover, recent work with patients following dorsal rhizotomy, a procedure that depresses spinal reflex pathways and results in reduced limb stiffness, indicates that some children who could not reciprocate prior to surgery were able to do so immediately after recovery without further therapeutic intervention. [36]

The preceding discussion is based on the assumption that a particular pattern of coordination (eg, reciprocal lower extremity movement or trunk rotation during reaching across the body) is available to a patient and can be produced if the proper conditions are set up, that is, if the appropriate control parameters are discovered and taken through a sufficient range of their values. It is expected that the newly elicited pattern will eventually become a reliable pattern of coordination for the behavior of interest. [4] The assumption is that the nervous system is capable of learning a desired pattern as a component of a particular motor act without a patient's specific intentional effort in the learning process. Thus, during treatment, while the therapist manipulates appropriate control parameters, a patient may be asked to creep across the room or to reach across the body to obtain an object or reward, without the patient's conscious effort to produce the appropriate relative timing pattern between the lower extremities, or the pelvis and trunk, respectively. Alternatively, therapy may be based on a belief that, to learn a particular pattern of coordination, the patient's conscious effort must be involved in the learning process, albeit with the therapist's assistance. [5] Will one approach lead to greater improvement in the patient's ability to produce more normal motor patterns than the other? Unfortunately, little comparative research is available that addresses this question.

Dynamic Pattern Theory may provide a useful framework for addressing such questions, however. Within this framework, for instance, it would be important to determine whether the desired coordination pattern is an intrinsic pattern, already within the system's capability, or whether it must be learned. If the latter were true, producing the desired pattern would require the patient's intentional effort to learn the pattern and the presence of information (eg, feedback) that is specific to the pattern to be learned. In DPT, such information is referred to as behavioral information (see "Self-Organization, Behavioral Information, and Learning"). [32] One might argue that if a coordination pattern cannot be produced already by the patient, then it cannot be an intrinsic pattern for the patient's damaged central nervous system. However, it may be that the pattern simply is not available to the system under the current conditions (eg, the limbs are too stiff or there is inadequate weight shift for reciprocal creeping to occur). That is, a behavior's intrinsic pattern dynamics may change depending on where the system is operating in control parameter space. This possibility has two important implications: (1) The more we are able to learn about the pattern dynamics for a behavior, the greater insight we should have about the required conditions for eliciting the desired pattern, and (2) to determine whether the pattern is available, the therapist must fully explore a behavior's control parameters. In other words, a therapist should determine the effect of modifying one or several modalities of input, perhaps as simple as changing the tone, speed, or loudness of one's voice when speaking to the patient or the firmness of the surface on which he is working, on the patient's movement pattern.

Pattern Stability and

Order-Parameter Fluctuations

The neuromuscular system is composed of many interacting components. We can recognize a particular spatio-temporal organization of those components as a pattern of movement (ie, a category of movement we call walking, reaching, etc), because it exhibits some degree of stability. Transient organizations of those components generally defy categorization. A pattern's stability, in turn, depends on the balance of cooperation and competition among its components. Because a system's components typically participate in the production of a number of different patterns (eg, neurons or neuronal assemblies as part of the pattern generators for different behaviors), with each pattern requiring different interaction dynamics, the stability of a particular pattern will depend on the nature of the forces tending to pull a component in one direction or another. For example, an anti-phase pattern of coordination of the hands requires a neural organization that produces simultaneous contraction of flexor muscles of one hand and extensor muscles of the other hand. If a pattern of neural input that tends to support simultaneous flexion of both hands influences the pattern generating networks, competition will be created. Such competition will result in variability of the component's behavior that may be observed macroscopically in the pattern of coordination itself. Although variability in performance often is considered merely as noise, which confounds our interpretation of a system's behavior, DPT views such variability (referred to in the theory as fluctuations) as an essential feature of a system's behavior that (1) can be used to estimate the stability of a system's patterns and, indirectly, the underlying cooperative processes; (2) reveals the nature of pattern change; and (3) actually may be necessary to prevent a system from becoming fixed in a particular pattern in order that it may change patterns.

Stability, then, is a key concept in DPT. Spontaneous transitions between patterns of movement, as from walking to trotting to galloping in quadrupedal locomotion, are believed to result from the loss of stability of the ongoing pattern as quantitatively changing control parameters (eg, the velocity of locomotion) approach critical values. [21,37] For example, the fact that the anti-phase pattern of hand coordination cannot be maintained at higher movement frequencies without significant effort on the part of a subject, and then only up to a point, suggests that this pattern actually loses its stability. Recent experiments [21,37] provide quantitative evidence for this loss of pattern stability. Thus, knowledge of a pattern's stability is essential for a full characterization of a system's movement pattern dynamics.

Two examples of stability measures are fluctuations in the value of the system's order parameter(s) and relaxation timeS. Fluctuations in the behavior and interactions of a system's components may be revealed as variability at the level of its order parameters, as noted previously. In Kelso et al, [37] the standard deviation of the relative phase between the hands was used as a measure of order-parameter fluctuations. The more stable the neuromuscular organization for the pattern, the smaller the standard deviation; a mean relative phase of 180[+ or -]4 degrees would indicate greater stability than a mean of 180[+ or -]25 degrees. In the bimanual experiments, the standard deviation of relative phase for the in-phase pattern was found to be relatively constant across all movement frequencies and smaller than that for the anti-phase pattern, indicating greater overall stability of the former patter. Moreover, the standard deviation for the anti-phase pattern increased with increasing movement frequency until the movement transition occurred, indicating a loss of pattern stability. Referring to Figures 2B and 2C, we can see the difference in the stability of the coordination patterns qualitatively. The magnitude of relative phase fluctuations prior to the transition, where relative phase is approximately 180 degrees, is clearly greater than afterward, where relative phase is approximately 0 degrees and the movement frequency is higher.

A second method for estimating pattern stability required perturbation of an ongoing movement pattern. The perturbation could take a number of forms as long as it is effective in disturbing the ongoing pattern. In the bimanual experiments, [21] we applied a torque through a handle that subjects held during hand oscillation in order to oppose the motion of one of the hands, hans changing the relative phase of movement between it and the other hand. The relaxation time is the time from the onset of the perturbation until the pattern existing prior to the perturbation is reestablished. That is, it is the time that it takes the system to "relax" back to its previous state. Note that this concept has nothing to do with muscle relaxation or reducing joint stiffness. A small relaxation time would indicate that the system recovers from the perturbation quickly and is relatively stable. Alternatively, long relaxation times would indicate a less-stable pattern. The relaxation times for the in-phase pattern of bimanual hand coordination were shown to be relatively constant for all movement frequencies. [21] Relaxation time increased, however, with increasing movement frequency for the anti-phase pattern of coordination, providing further support for the prediction that loss of pattern stability is a critical factor leading to spontaneous transitions between movement patterns. Thus, by identifying a system's order parameters, estimates of a pattern's stability become possible as a means of characterizing a behavior's pattern dynamics. Proper interpretation of those dynamics, however, also requires knowledge of the status of a system's control parameters.

Therapeutic implications. Given that order parameters for a motor act can be identified, measures of pattern stability related to those parameters are already well defined. Such measures can be used to differentiate among the stability of different patterns for the same act or to document changes in a particular pattern's stability as conditions of performance change. Consider again the child with spastic diplegia who bunny-hops in order to move about. As the result of treatment, the child may begin to locomote with a reciprocal lower extremity pattern at low movement velocities. Improved performance will be indicated by the child's ability to creep at higher movement velocities (eg, the ability to produce adequate weight shift as the speed of movement increases). Yet, before the child can extend the range of velocities over which he or she is able to creep, significant improvement in the pattern's stability at lower movement speeds may occur. With the appropriate measures, one should be able to document such improvement quantitatively.

We could measure, for example, the variability in the relative timing among the limbs over several cycles of locomotion. Alternatively, we might administer a perturbation to disturb the pattern, during which a number of factors would have to be controlled for, including the phase of the movement cycle at which the perturbation is applied. This perturbation could take the form of a mechanical perturbation (eg, by briefly restraining one lower extremity or abruptly and transiently changing the speed of a treadmill on which a patient is creeping). [38] In either case, the time required for the patient to return to a stable reciprocal creeping pattern could be used as an estimate of the pattern's stability. The strength of the perturbation might need to be small initially, because if it led to a transition to the hopping pattern, the patient might be unable to reestablish the reciprocal pattern independently. However, this fact, in itself, would be indicative of the pattern's relative instability. One also might vary the strength of the perturbing stimulus to determine how strong it has to be before such a transition is induced. An increase in the strength of a perturbation at which the patient can maintain the desired pattern would also indicate improved pattern stability.

An additional measure of a pattern's stability is the switching time that can be applied to either spontaneous or voluntary pattern switching. For example, if a patient were practicing creeping, we could measure the time that it takes for the patient to revert to the bunny-hop pattern after beginning to creep. As the creeping pattern becomes a more stable pattern for the patient, the spontaneous switching time should increase. Of course in many, or perhaps even most, clinics not associated with a motion analysis laboratory, obtaining quantitative measurements of relative phase variables in order to measure their stability may not be feasible. Therefore, a simple qualitative example of how the creeping pattern might be analyzed in a manner consistentwith this approach is presented in Figures 3A and 3B. For this example, a 5-year-old patient with spastic diplegia who had just recently begun to exhibit the reciprocal creeping pattern was filmed while moving on all fours across a room. Afterward, the positions of the contact points of each limb (ie, the knees and the hands) were digitalized using a motion analysis system. However, the same objective could have been obtained by applying contact switches to the contact points of the limbs and recording their output. Figure 3A is a plot (the generic term for such a plot is a Lissajou figure) of the resultant position of one limb against that of the homologous limb for both the upper and lower extremities. Note that time is implicit in this figure; that is, each coordinate or sample represents the resultant position of two limbs at the same point in time. Figure 3B is a similar plot for diagonal limb pairs. Figure 3A provides us with a method for evaluating the pattern of interlimb coordination at each girdle, whereas Figure 3B gives a qualitative picture of forelimb-hindlimb coupling.

For the reciprocal creeping pattern, we would expect the plot for homologous limbs to approximate a staircase. That is, while the contact point of, say, the right upper extremity is moving forward during swing, the left limb should be extending while its contact point remains stationary. Rounding of the staircase would occur if the relative phase of the limbs' motions was not exactly anti-phase. During the bunny-hop, however, homologous limbs are both either swinging forward or maintaining a stationary contact point while extending. A Lissajou plot of this pattern should approximate a diagonal line. Reference to Figure 3A reveals that, for the upper extremities, a reciprocal pattern was produced throughout most of the analyzed sequence, although the patient reverted to the in-phase pattern briefly near the middle of that sequence. The lower extremities, on the other hand, alternated between in-phase and anti-phase coordination, revealing the apparent instability of the latter pattern. Instabilities at cretain points in this record are also noticeable.

Figure 3B reveals that both diagonal pairs of limbs maintained the staircase pattern throughout this sequence. Drawing an analogy with quadrupedal gait patterns, this pattern of diagonal limb coupling would be expected for either reciprocal walking or galloping (ie, bunny-hopping) but not for trotting (analogous to mature creeping), where diagonal limbs should move simultaneously.

The point of this illustration is that such an analysis could be used to determine how long the reciprocal, or anti-phase, pattern could be maintained after beginning to creep before switching to the bunny-hop, or in-phase, pattern. Moreover, the number of times that the patient exhibits switching between the patterns for a given time interval may itself be a useful index of the pattern dynamics for quadrupedal locomotion. Once the desired pattern can be established at a particular movement frequency, the patient could be asked to switch intentionally between patterns on command and the time required to do so measured. [33] As the desired pattern becomes more stable, the time required to switch to this pattern should decrease (ie, intentional processes are predicted to be influenced by the intrinsic pattern dynamics). Proper interpretation of any of these measures, however, will require information about the status of the system's control parameters. For example, if movement speed is an important control parameter for the behavior, estimates of pattern stability that are made while the movement frequency is actually changing would be extremely difficult, if not impossible, to interpret.

Time-Scale Relations

The stability of a behavior's coordination patterns is defined fully only in the context of a number of important time scales and their relations. Temporal parameters of interest include the time over which the system's behavior is observed, the time scale of change of control parameter values, equilibration time, and pattern relaxation times. A full description and explanation of these time scales and their relations was given by Jeka and Kelso. [34] A more detailed mathematical account was presented by Schoner et al. [18] Three such time scales will be considered in this article.

The time scale of change of control parameter values [([tau].sub.par.)] describes how rapidly the control parameter value for a particular behavior is changed, which will influence the nature of transitions between a behavior's coordination patterns. [19,39] For example, if movement frequency is a control parameter for bimanual coordination, a relatively fast time scale would exist if frequency was changed continuously or rapidly (et, [[tau].sub.par]=2 seconds). If the same frequency was maintained for a long time period (et, [[tau].sub.par]=10) seconds) before it was changed, the time scale of parameter change would be relatively slow.

Relaxation time [([tau].sub.rel.)] was defined previously as the time required to return to an ongoing pattern of coordination after that pattern's disruption and has no meaning independent of a specific movement pattern. Perturbations of a pattern result not only from extrinsic stimuli such as a mechanical impulse applied to a limb, but also from fluctuations in the behavior of the pattern's underlying components. A short relaxation time for a pattern indictes that the effect of such fluctuations on the pattern's dynamics are minimal, because the system will return quickly to its previously mean state. As relaxation time increases, however, the pattern will appear more unstable. For a detailed theoretical model, see article by Schoner et al. [18]

Equilibrium time [([tau].sub.equ.)] is the time required for a system to "seek out" or establish its most stable pattern of coordination for a given behavior and is related to the switching time discussed in the previous section. Consider a horse moving about in an open field. According to DPT, the likelihood that one will observe the horse walking, trotting, pacing, or galloping is a probabilistic function of the stability of those patterns of inter-limb coordination, given current control parameter values (eg, velocity of locomotion). Given enough time, it is predicted that patterns of increasing stability will be adopted. That is, if animals or humans adopt a pattern of coordination that is less stable than others available for a behavior, they will eventually switch to a more stable pattern. Such pattern changes are assumed not to require intentional intervention. However, subjects can intentionally maintain a less stable pattern up to a point, delaying the occurrence of a spontaneous pattern transition. (Even if this were to occur, however, the stability of the behavior would be affected by the intrinsic pattern dynamics. [33]) The idea that systems will move toward states of increasing stability, and typically less complexity, is not unique to this theory. Early in this century, Erich von Holst concluded this idea from his studies of the coordination of a variety of animal behaviors. [40]

The important point is that what one observes when studying a particular behavior will depend on the relation among these different time scales, particularly when control parameters are being changed. Consider an example for bimanual coordination. Suppose that we wanted to determine the stability of the anti-phase ([Phi][is nearly equal]180[degrees]) coordination pattern at different values of the control parameter (ie, movement frequency) by measuring relative phase fluctuations (ie, the standard deviation of the relative phase). We have the subject begin a trial in this pattern of movement at a low frequency and then systematically increase the frequency in equal steps. However, suppose that we choose the time scale for parameter change to be very small. That is, we change the movement frequency very rapidly, say every 2 seconds. The change in movement frequency may itself act as a perturbation to the ongoing pattern of coordination, resulting in a transient increase in relative phase variability. If the time scale of parameter change is too small, however, inadequate time for recovery may occur before the frequency requirement is again changed. Therefore, an analysis of relative phase fluctuations may suggest that there is no difference in the stability of the anti-phase pattern across levels of the control parameter or compared with the in-phase pattern examined under similar circumstances. If instead the control parameter were changed more slowly [([tau].subpar.larger)], larowing time for the pattern to reach its steady state after the frequency change, then a difference in the stability of the pattern at different values of the control parameter or compred with the in-phase pattern might become apparent. [39]

As another example, consider the relation between the relaxation time for a pattern [([tau].sub.rel.)] and the behavior's equilibration time [(tau].sub.equ.)]. The magnitude of these variables at any point in time and, therefore, their relationship, is dependent on the value of the control parameter. At a low movement frequency, the relaxation time of the anti-phase pattern of hand coordination is relatively small (ie, the system will recover quickly from a perturbation). At the same time, the behavior's equilibration time, or the time predicted to take for the hands to spontaneously adopt the slightly more stable in-phase pattern, is quite large. That is,

(2) [[tau].sub.rel] * [tau.sub.equ]

and the anti-phase pattern will appear to be stable for a relatively moderate observation period. As the movement frequency is increased, the time required for the anti-phase pattern to recover from a disturbance [([tau].sub.rel.)], whether resulting from an extrinsic perturbation or from fluctuations in the behavior of the hands' neuromuscular components, also will increase. The pattern will appear increasingly unstable. Moreover, the equilibration time will become smaller. Thus, for larger values of the control parameter, or higher frequencies of movement, the gap between these two time scales will narrow:

(3) [[tau].sub.rel] [is less than or =] [[tau].sub.equ]

Therefore, the probability of witnessing a spontaneous switch to the more stable in-phase pattern increases with increases in movement frequency. That is, if we watch the subject perform the anti-phase pattern for a relatively long period of time, there is a higher probability that we will see the pattern of coordination switch to an in-phase pattern if movement frequency is high than if it is low. If we do not observe the system for long enough, however, we may fail to observe this difference in pattern stability at the lower and higher values of the control parameter (ie, the observation time is also important for determining the system's stability). Eventually, for very high frequencies of movement, the relaxation time for the anti-phase pattern becomes extremely large such that.

[T.sub.rel] [is nearly equal] [T.sub.equ]

and the more stable in-phase pattern of coordination will be adopted almost immediately.

Therapeutic implications. although this formalism may appear at first to have little more than didactic value, an understanding of these time-scale relations has practical significance. For example, by modeling these time-scale relations for the bimanual coordination experiments, predictions about the system's behavior were generated, [18] subsequently tested experimentally, [21, 37] and corroborated. Independent of the need to extend such modeling to the behaviors produced by individuals with a damaged nervous system, an application of these time-scale relations to therapy may lead to important insights.

Consider again the patient with spastic diplegia whos dominant mode of locomotion is the bunny-hop. Ignoring the upper extremities for the sake of simplicity, we can assume that this pattern, involving in-phase coordination of the lower extremities, is more stable than the desired reciprocal creeping pattern, and anti-phase pattern of lower extremity coordination. In fact, because the latter pattern is not seen, we can assume that it is not available to the system at the observed control parameter values. Manipulating certain parameters through our handling techniques may lead the patient to adopt a reciprocal lower extremity pattern resembling normal creeping. However, assume that the patient can maintain this pattern only at rather low movement frequencies. If guided practice of the reciprocal pattern leads to its improved stability so that time-scale relation (2) obtains for low speeds of creeping, the patient should practice this pattern in treatment and avoid the bunny-hop pattern. Suppose, however, that although time-scale relation (3) is operative at a moderate speed of locomotion, time-scale relation (4) is operative at a speed that is only slightly higher. To extend the range of control parameter values over which the patient can perform the reciprocal pattern stably, practice must occur at the higher speed of locomotion. If the patient practices at this speed for any length of time, however, a transition to the bunny-hop pattern is predicted to occur, because the system will seek out its most stable pattern. The time required for this transition ([T.sub.equ]) is relatively short compared with the reciprocal pattern's relaxation time. Thus, the time during which the patient practices at the higher speed should be limited to relatively brief periods, perhaps moving quickly between the higher speed and the lower speed, until the pattern becomes more stable at the higher speed (ie, time-scale relation [2] is operative). Thus, knowledge of how such time-scale relations affect a system's behavior can be used to guide the plan of treatment.

Self-Organization, Behavioral

Information, and Learning

In the context of DPT, spontaneous pattern change is assumed to result from the self-organization of appropriate neuronal networks that underly the behavior of interest. Self-organization implies that a pattern is neither imposed or commanded (eg, by higher nervous centers) nor a feature of the network's specific anatomical structure, but results from the dynamics of the interactions between components of the network under the influence of inputs from both higher brain centers and the periphery. A particular neural network may be involved in the generation of several similar patterns, and several such networks may be capable of generating the same pattern. This implies that some degree of indetrminacy exists with respect to inputs that activate the pattern-generating networks. The results of recent behavioral work on bimanual and similar pattern transitions [21, 30, 35, 37] contain many of the signature features of self-organization. [19] There also exists evidence for self-organization at both neural and cognitive levels of functioning. [41-44] For instance, even in a relatively simple nervous system, such as that of the seal slug Pleurobranchaea california, knowledge of the speciic neural connections among neurons cannot necessarily predict the activity of these neurons during motor pattern generation. [43] The activity of neural networks producing feeding behavior in this animal is marked by nonlinearities and depends on the network's activation history. Production on different feeding behaviors is thought to occur as functional neurocircuits "emerge or 'self-organize' dynamically from the underlying neural connectivity." [43] (p512) That is, the pattern generating network does not "contain" a particular pattern in its structure. The pattern emerges, instead, as a temporary manifestation of the dynamics of the network, that is capable of producing multiple patterns under different conditions (eg, depending on the nature of the inputs or the network's activation history). Note that the requirements for self-organization include a relatively large number of system components and nonlinear behavior of those components, both of which are characteristic features of the neuromuscular system. Therefore, the large number of degrees of freedom of the neuromuscular system is no longer a problem, but a necessity in this context.

Earlier in this article, I suggested that many of the basic movement patterns we attempt to elicit from patients actually may be intrinsic patterns for the system. That is, the patterns may already be available for the behavior but are not produced because of a failure to access appropriate control parameters or to take these parameters to a critical value. These control parameters may take the form of central nervous system influences on the brain stem or spinal pattern generating networks whose dynamics lead to the pattern's production. for example, the inability to produce adequate weight shift in sitting may prevent a pattern of trunk rotation from emerging when attempting to reach across the midline. By making use of segmental inputs, the therapist may be able to tap other control parameters to facilitate production of the desired pattern in conjunction with the patient's effort. assuming that this facilitation is possible, the question remains: How does the patient eventually learn to produce the pattern without the influence of inputs provided by the therapist?

One can only assume that the nervous system will undergo reorganization as the result of experience and will learn new ways to access the relevant control parameters or to find new control parameters for the behavior. What this translates into at the neural level is unclear, but is likely to be related to known mechanisms of neural plasticity. [45] Recent animal research indicates the dynamic nature of brain function and suggests that self-organization is an important feature of those dynamics. For example, electrophysiological work on thes reorganization of cortical sensory fields in primates has shown that dramatic shifts in these fields can occur following cutting of a peripheral nerve. [46] Moreover, following nerve regeneration, the cortical fields appear to reassume an organization similar to that existing prior to nerve injury. In addition, recent cross-innervation studies on the cat hind limb [47] and, more dramatically, on the monkey forelimb, [48] have shown how dramatically the brain can reorganize synergies of movement so as to preserve near-normal function. Adequate experience likely will be important to facilitate appropriate brain reorganization. [49] If therapists can identify and manipulate appropriate control parameters to facilitate the emergence of a more normal coordinative pattern for an act, perhaps the resulting pattern of affarent input will contribute to the process of brain reorganization. This hypothesis is, of course, in need of direct experimental testing. Making a patient consciously aware of those parameter manipulations that are effective may also help in the learning of a new strategy for eliciting the pattern indpendently. Thus, for example, if increased weight shift is critical for producing reciprocal lower extremity movement in creeeping, or for eliciting trunk rotation in sitting, it may be helpful to draw the patient's attention to how changing this input affects performance.

It is likely, however, that many patterns of coordination are not intrinsic patterns; that is, there are no control parameters of which direct manipulation will lead to that pattern's spontaneous production. Most skilled movement patterns used in sports are initially of this nature. The process of learning to produce such patterns requires the conscious effort and close attention of the learner. It may be the case that some movement patterns that are intrinsic patterns for the healthy individual no longer are available to an individual following brain injury. In this case too, a patient's intention is likely to be required in order to relearn the pattern. However, until adequate effort has been made to elicit the desired pattern spontaneously by mamipulating appropriate control parameters, it cannot be determined unequivvocally that intentional effort is a necessary condition for the pattern's production.

The foregoing discussion suggests that a potentially useful distinction exists in learning to produce a pattern of coordination for a motor act. If the desired pattern is already an intrinsic pattern of the system, the learner must learn to tap an appropriate control parameter that will lead to the pattern's spontaneous production. The alternative is that the pattern itself must be learned. The type of information (eg, feedback) that an individual needs in order to learn in these two instances may be quite different and is open to investigation.

According to DPT, the process of learning a new pattern involves a modification of the system's intrinsic pattern dynamics. That is, as learning occurs, the new pattern becomes an integral part of those dynamics. Once this modification occurs, spontaneous generation of the new pattern should be possible theoritically under the appropriate conditions (ie, critical values of appropriate control parameters). If an individual is to learn a new pattern of movement, however, he or she must be provided information about the required pattern and his or her performance (ie, feedback). but what form must this information take? It is logical to assume that the information provided cannot be arbitrary, but must be functionally specific to the dynamics that are to be modified, if it is to be successful in attracting the system toward the new pattern of coordination. In the case of movement patterns, order parameters can be identified to characterize the behavior's patterns of coordination. Therefore, in order to be effective, information should be specific to the order parameter dynamics. In DPT, such information is referred to as behavioral information, because it is specific to the behavioral pattern of interest. Let us consider a simple example.

Only the in-phase and anti-phase patterns of bimanual coordination can be produced stably by most individuals in the rhythmic movement paradigm described earlier. [15] If subjects are asked to produce other bimanual patterns, relative phase variability is extremely high, indicating a very unstable pattern, and the pattern actually produced is closer to once of the system's intrinsic patterns than to the required pattern. [22] For example, if a subject is asked to produce a relative phase pattern of 30 degrees, that pattern actually produced will be nearer to a relative phase of 0 degrees. If the required relative phase is 150 degrees, the subject will produce a pattern closer to 180 degrees. A required relative phase of 90 degrees will be attracted to a relative phase of 0 degrees rather than 180 degrees, because the former pattern is the most stable intrinsic pattern. [21,37] However, with appropriate practice, subjects can learn to produce a previously unstable pattern (eg, [Phi]=90[degrees]) so that is now becomes a stable pattern of coordination for the behavior. [32] In these recent experiments on the dynamics of learning, the information provided to subjects during practice was in the form of computer displays that informed the subjects of the actual relative phase of motion being produced between the hands. Thus, a form of visual biofeedback provided specific information about the order parameter, or the relative phase of component motions, for the behavior.

Therapeutic implications. Once an appropriate control parameter for an act has been identified that, when manipulated, leads to consistent and automatic elicitation of a desired pattern of coordination, making patients aware explicitly of the effective pattern of input may help them to identify internal control parameters that will be effective in eliciting the pattern. The information provided by the therapist should, theoretically, be related to the control parameter(s) used by them to elicit the behavior. Whether such information is helpful to or necessary for the patient to find strategies to elicit the pattern independently is open to experimental testing. For example, if a patient can learn to produce a controlled weight shift in sitting when reaching across the midline of the body, trunk rotation may follow automatically.

If, instead, exploration of potential control parameters for an act fails to elicit a pattern spontaneously, the volitional effort of the patient to produce the pattern will likely be required if learning is to occur. The therapist's role, in this instance, will be to provide appropriate behavioral information to guide the learning process. This information should be related to the order parameter(s) for the act. Thus, it will be important to (1) identify appropriate order parameters for the behavior and (2) provide information in the form of those parameters. Once identified, it also will be important to determine whether one feedback modality (eg, visual, auditory, kinesthetic, or some combination thereof) enhances learning more than another. This will depend, in all likelihood, on the behavior for which the pattern is to be learned. Nonetheless, by identifying order parameters for the behavior, the effect on the learning process of different modalities and of the information strength is potentially quantifiable. For example, if the relative phase of motion between the movement components were an order parameter for the act, the different between the required relative phase (ie, the pattern that the patient attempts to produce) and actual relative phase would provide a measure of the effectiveness of the modality or strength of the behavioral information. [32]

Summary and Conclusions

Recent research [21,37,39] has shown that pattern change can occur as the result of a loss of pattern stability, as evidenced by enhanced order-parameter fluctuations and increased pattern relaxation times, that occurs when important control parameters reach critical values. That is, pattern change may occur spontaneously in many instances without a specific intention to produce such a change. In addition, observed changes in order-parameter fluctuations and pattern relaxation times represent the signature features of self-organization. [19] The results strongly suggest, therefore, that patterns can arise as the direct result of a pattern-generating network's intrinsic dynamics and need not be imposed on the network by specific commands from higher nervous centers. If so, the possibility exists that, in patients with movement incoordination resulting from brain injury, reorganization of intact neural centers may be able to substitute for damaged centers normally responsible for producing the control parameter changes that lead to spontaneous pattern generation in brain-stem and spinal networks. Because DPT's emphasis is on characterizing patterns and their dynamics at any scale of observation, this theory may provide more useful insights to therapists attempting to influence pattern change than might other theoretical approaches to motor control.

The basic tenets of DPT that have immediate applicability to therapeutics can be summarized as follows:

1. Order parameters macroscopic observables that can be used to characterize the dynamics of a behavior's patterns, whether normal or abnormal.

2. Measures of order-parameter stability may be used to characterize the differential stability of different coordinative patterns and to study changes in pattern stability that occur with continuous changes in other extrinsic variables. These measures include (1) order-parameter fluctuations, (2) pattern relaxation times, and (3) switching times.

3. A spontaneous transition from one movement pattern to another may occur when key control parameters reach critical states or parameter values. Therefore, identifying and manipulating the control parameters for a behavior is critical if one wishes to elicit spontaneous pattern change.

4. The nature of pattern change and of a pattern's stability depends on important time-scale relations, including the time scale of control parameter change, observation time, pattern relaxation times, and the global equilibrium time for the behavior's patterns. Attention to these time-scale relations in treatment will provide an effective framework for training and evaluation of desired movement patterns.

5. A determinationof a behavior's intrinsic pattern dynamics is necessary before the effect of specific intentional influences can be understood.

6. Intentional pattern change involves modification of the intrinsic pattern dynamics for an act and requires behavioral information that is specific to those dynamics. In order to optimize the learning of a new pattern of coordination, information should be provided to the learner in the form of the behavior's order parameter(s).

7. The effect of the modality in which behavioral information is provided to the learner or the strength of that information on performance of a new pattern can be evaluated by measured (1) order-parameter fluctuations and (2) the difference between the required value of the order parameter(s) and the actual value produced by the patient.

The development of DPT is still in its early stages. The review provided herein touches on but a few of the basic constructs of the theory related to pattern dynamics. Applications to movement dysfunction must proceed with caution at this time. Nevertheless, a number of implications derived from the theory may support treatment strategies already in place and, more importantly, provide new insights for the future development of such strategies. An important feature of DPT is its emphasis on a close theory-experiment relationship. It is important that this same emphasis be carried through in applications to clinical practice.

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JP Scholz, PhD, PT, is Assistant Professor of Physical Therapy, School of Life and Health Sciences, 009 McKinly Laboratory, University of Delaware, Newark, DE 19716 (USA). (BITNET: AEJ03058@UDACSVM.)